Fn3410321036

Ghanshyam Gagged, Krishnakant Pandey, Shubham Asati, Jaisankar N / International
Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622
www.ijera.com Vol. 3, Issue 4, Jul-Aug 2013, pp.1032-1036
1032 | P a g e
Parallelization of Cryptographic Algorithm & Key Identification
Using Genetic Algorithm Approach
Ghanshyam Gagged, Krishnakant Pandey, Shubham Asati, Jaisankar N
School of computer science & Engineering, VIT University, Vellore-632014, Tamilnadu, India
Abstract
Now days, the amount of transfer of data
over large network is increasing day by day. As
there is increase in data transfer, simultaneously
there are security threats that are arising with it.
In this paper we are proposing cryptographic
systems that make use of genetic algorithm to
securely transfer the data over large network.
This approach helps us to provide high
achievability to transfer data securely. The
techniques that we are using for encryption &
decryption are based on genetic algorithm which
will help us to efficiently encrypt the data which is
resistible for any kind of external attacks. Then
we will parallelize it using Open Mp language
which accelerates the transformation of data to
achieve high security. Then analyze the
performance for both code serial and parallel
execution.
Keywords: The genetic algorithm, Linear
generation Equation, Genetic operator, Open MP
I. Introduction
We know that, Cryptography is the study of
encrypting the information & producing
incomprehensible data which is unreadable by the
third person who is accessing data without prior
permission of sender or receiver. Now a day various
application like the social networking, business
applications, E-commerce, in military or satellite
communication etc need lot of data transmission over
large data network. Here is the main concern for
privacy comes into picture. As the above said areas
are very much vulnerable to attacks many researchers
are working on it. We already have many algorithms
for encrypting & decrypting the data. Encryption is a
process of transferring simple text into cipher text
and decryption is a process transferring cipher text
into simple text which is readable and generate a key
which is a shared between processes of cryptography
[9]. Encryption and decryption are opposite to each
other for transforming data. The genetic algorithm
that we are using takes combination of features of
cryptography and genetic operator. The genetic
operators that we are using are crossover & mutation.
In crossover we combine two strings to get the new
better string. The mutation is the process of changing
any bit from the given set of bits. So here we can use
the concept of Open Mp to parallelize the code. The
generation of random number can also be parallelized
so we will always get different randomized number
from different-different threads. Here we are using
the concept of symmetric key.
Fig.1 Symmetric key encryption & decryption
In the cryptography there are two types by
which we can encrypt and decrypt the text i.e.
symmetric and asymmetric key. The cryptographic
system in which sender & receiver use the same key
for encryption & decryption data is called symmetric
key cryptography [1]. The Cryptographic system in
which sender and receiver use the different key for
encryption & decryption data is called asymmetric
key cryptography. As we know the data to be transfer
is very large we need very efficient & fast algorithm
to encrypt or decrypt it [9]. The parallelization of
genetic algorithm yields better performance that will
be very useful for transferring large data securely
using this parallelized code. Now we will discuss all
the issues in detail.
II. Linear generator Equation
Firstly here we a creation a sequence of
random number by using Congruential method then
next generation number random number with the help
of Crossover and Mutation which is a operator for
genetic algorithm.
Xn+1 = (a * Xn + C) mod m; ......(1)
Xn= a randomly generated value initially it is
assume.
a= multiplier which randomly generated
c= increment which randomly generated
m= modulus (0<m<10)
Message in
Plain text
Message in
ciphertext
Message in
Plain text
Message in
ciphertext
Encryptio
n
decrypti
on
Insecure network

1033 | P a g e
III. Generic Operators:
From the three operators of genetic
algorithm i.e. CROSSOVER, SELECTION and
MUTATION [6] here we will be using only two
operators i.e. Crossover and Selection for our
purpose.
A. Crossover
It is a genetic operator which is used to join
two strings to get an efficient string. In this process
we take more than one parent process and generate a
child solution for that process [2] this crossover
genetic operator generate random number which
perform in parallel.
There a three types of crossover [6]:
 Trade of uniform crossover
 one site Crossover
 Cut and splice
In this paper we will be concentrating on
one site Crossover. This method is selected because
of its advantage over traditional methods that we can
easily exchange information through it very
effectively as per our requirements.
We know that the data while transferring is
converted into bits and then sent over the network so
our next method i.e. MUTATION changes any bit
randomly from the set of bit to achieve high security.
As the bits are changed its very difficult for intruder
to withdraw the information from it. As we are going
to parallelise the code the different thread will play
very vital role in changing the bits.
IV. CRYPTOGRAPHY: GENETIC
ALGORITHM APPROACH
3.1. Algorithm
3.1.1 Generation Linear Equation of First order
using Random Number [7]
In this we use Linear Equation for
generating first order variables [5]. Initially we will
consider four random variable a, c, m. Xn. Now as per
our formula of generating linear equation we will
substitute this assumed 4 values to calculate next
value. After that iteratively we will put the value of
Xn+1 that is generated from the previous calculation.
This iterative process will terminate only when it will
complete the iterations equal to the length of the
message. Here we can see that the initial parameters
are unchanged throughout the process. A good
randomization function must be used to get better
initial values [6].
3.1.2 Crossovers and Mutation:
After the above defined process we have
some random numbers generated that are equal to the
length of message. Now this numbers are converted
into binary formats and length of each binary number
is equated by padding some zeros at the beginning of
that number[4]. Now here we will be using the
crossover operation of genetic algorithm in which we
will swap some bits of one string with the other
string. At this stage two numbers are differently
changed from their initial values to the new values.
Let’s illustrate it with an example.
Consider two numbers of 8 bit,
187 10111100 10000100
132 10000100 10111100
As of now we have just performed crossover now we
will deal with mutation. Mutation is the process of
changing the bit from the available set [3]. Here is the
main function of mutation operator to change the bit
any the selection of bit which is to be changed is
done probabilistically so security increases. Finally
after performing Crossover & mutation for several
iterations we will get series of randomized number
that we will again convert into decimal format for our
further use.
Now the numbers which we will get finally
will be in decimal format, so we will select the
smallest number from it & the specific digit that is
mutually decided between two parties will be
subtracted from the ASCII value of our text message
and the number which we will get after that is sent
over the network along with the key.
3.2. For Example
3.2.1 Encryption
In this method the simple text converted into cipher
text, using above algorithm
 Let, message is ABCDEFGHIJ its length is
10.
 Now applying linear Congruential equation,
we will get the generated numbers that are
similar in length of text message i.e.10.
Let, numbers are: 106, 239, 538, 1211, 2725, 6132,
13798, 31046, 69854 and 157172. Now, Select two
numbers from a group that starting (106,239), (538,
1211), (2725, 6132), (13798, 31046), (69854,
157172).
Then apply crossover and mutation iteratively:
106= 0000000001101010
239=0000000011101111
After performing crossover
0000000101101010 =362
0000000111101111=495
Now we identify that some binary digits
have been changed. Performing mutation
0000000110001010 =394
0000000100001111= 271
After applying mutation, numbers are (394, 271).
Now we easily identified how group pair is
changed from (106,239) to (394,271). However we
find that both crossover and mutation increases
security and after performing some iteration the
whole data become secure.
Now after first iteration of crossover and
mutation number will be obtained
(394, 271, 1018, 1371, 2885, 5652, 13318, 30886,
35215, 39069)

1034 | P a g e
Now took a smallest number i.e. 271 and subtract
second right digit from ASCII values of each
character of message.
Input
Data
Ascii
Values
Generated
number
Number
to be
subtracted
Cipher
text
A 65 394 9 56
B 66 271 7 59
C 67 1018 1 66
D 68 1371 7 61
E 69 2885 8 61
F 70 5652 5 65
G 71 13318 1 70
H 72 30886 8 64
I 73 35215 1 72
J 74 39069 6 68
Table 1 Encryption procedure
The encrypted message is > @CA=@D@GJ
The Cipher text :{ 56,59,66,61,61,65,70,64,72,68
{key of {a, c, m, Xn }}
3.2.2 Decryption
At a user side we get a whole encrypted data
along with key {a, c, m, Xn}. As we know decryption
is an opposite process of encryption for that a
receiver side inverse of encryption will be perform
[8]. After that many iteration perform in decryption
as they performed in encryption using cipher key.
Cipher
text
Number to be
added
ASCII
Values
Input
Data
56 9 65 A
59 7 66 B
66 1 67 C
61 7 68 D
61 8 69 E
65 5 70 F
70 1 71 G
64 8 72 H
72 1 73 I
68 6 74 J
Table 2 Decryption procedure
V. RESULTS
As our main aim is to parallelize the
program to get fast output according to that we tested
it for various number of file size. Here we present the
table representing the throughput and the graphical
representation with core different core processor.
A) For 2 core machine:
File Size Serial
Execution
Time
Parallel
Execution
Time
Speed Up
1MB 0.33ms 0.19ms 1.67
10MB 1.5ms 0.82ms 1.81
50 MB 11.2ms 5.6ms 2
100 MB 21.4ms 9.5ms 2.25
150MB 37.3ms 13.4ms 2.78
B) For 4 core machine:
File Size Serial
Execution
Time
Parallel
Execution
Time
Speed Up
1MB 0.33ms 0.11ms 3
10MB 1.5ms 0.48ms 3.12
50 MB 11.2ms 2.71ms 4.12
100 MB 21.4ms 3.4ms 6.3
150MB 37.3ms 4.72ms 7.89
C) For 8 core machine:
File Size Serial
Execution
Time
Parallel
Execution
Time
Speed Up
1MB 0.33ms 0.07ms 4.67
10MB 1.5ms 0.28ms 5.2
50 MB 11.2ms 1.49ms 7.51
100 MB 21.4ms 2.4ms 8.9
150MB 37.3ms 3.49ms 10.67
D) Performance Analysis:
File Size 2 Core 4 Core 8 Core
1MB 1.67 3 5.67
10MB 1.81 3.12 6.2
50 MB 2 4.12 8.51
100 MB 2.25 6.3 9.9
150MB 2.78 7.89 11.67
Table 3 Performance analysis
We can see that parallelized program with
different core processor which gives better output in
terms of time taken for execute.

1035 | P a g e
Fig 2 Graph showing the perfomance analysis
As we can see from the performance of our
algorithm on different-different cores we can predict
the future speed up for given large size of file.
Fig 3 speed up Curve for known file size
By looking in this graph, we say that the
speed up factor is seems to be increasing as file size
is increase in a constant growth rate. Now we are
using logarithms for transfroming this equation into
linear equation.
The linear equation is as follows,
Y = m + cX ....(2)
Where,
c = constant
m = speed up factor
Projected values
File Size 8 Core Projected
Values
1MB 5.67 5.67
10MB 6.4 6.4
50 MB 8.51 9.64
100 MB 9.9 13.69
150MB 11.67 17.7
200MB - 21.81
300MB - 29.92
400MB - 38.01
500MB - 46.13
Table 4 projected values
Fig 4 Speed up curve for projected values
Proof:
We can prove it by using mathematical
formula. Lets consider the speed up on 8 core
machine for a given size file then it will follow the
equation (2) i.e.
Y = c + mX
Solution: We will use mathematical induction for
proving the above statement.
For 8 core machine,
Lets take initial values of X & Y
Y = 5.67 for file size of X = 1MB
Y= 6.4 for file size of X = 10MB
Putting this value in our equation,
We will get,
c = 5.58, m = 0.0811.
so now extending it to size of 100MB, 150 MB it
comes true.
For all values it will come true so we can say that this
equation holds for all given size of file.
VI. Conclusion
We can see that the genetic algorithm
operator that we have used gives better performance
as compared to other algorithm. If we write the same
alphabet in our message like ZZZZZZ still it will
generate different key and the value for each
alphabet. The number of times we iteratively repeat
the process of crossover & mutation we would be
keep getting more secure encryption. Even successful
parallelization yields better results in terms of
execution time. As we have not yet used all the
operations of genetic algorithm in future we can used
it get better security.
References
[1] Benjamin Arazi, “Vehicular
Implementations of Public Key
Cryptographic Techniques”, IEEE
TRANSACTIONS ON VEHICULAR
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150 KB 5 MB 25 MB 50 MB 100MB
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8 Core

1036 | P a g e
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